Then he sat down, fanned himself with a handkerchief, and continued. “Then, of course, we keep the whole thing in another box that’s so small you can’t see it—and, if you follow me, I’ll show you where to find it.”

They walked to one of the small windows and there, tied to the sill, was one end of a line that stretched along the ground and into the distance until completely out of sight.

“Just follow that line forever,” said the Mathemagician, “and when you reach the end, turn left. There you’ll find the land of Infinity, where the tallest, the shortest, the biggest, the smallest, and the most and the least of everything are kept.”

“I really don’t have that much time,” said Milo anxiously. “Isn’t there a quicker way?”

“Well, you might try this flight of stairs,” he suggested, opening another door and pointing up. “It goes there, too.”

Milo bounded across the room and started up the stairs two at a time. “Wait for me, please,” he shouted to Tock and the Humbug. “I’ll be gone just a few minutes.”

Up he went—very quickly at first—then more slowly—then in a little while even more slowly than that—and finally, after many minutes of climbing up the endless stairway, one weary foot was barely able to follow the other. Milo suddenly realized that with all his effort he was no closer to the top than when he began, and not a great deal further from the bottom. But he struggled on for a while longer, until at last, completely exhausted, he collapsed onto one of the steps.

“I should have known it,” he mumbled, resting his tired legs and filling his lungs with air. “This is just like the line that goes on forever, and I’ll never get there.”

“You wouldn’t like it much anyway,” someone replied gently. “Infinity is a dreadfully poor place. They can never manage to make ends meet.”

Milo looked up, with his head still resting heavily in his hand; he was becoming quite accustomed to being addressed at the oddest times, in the oddest places, by the oddest people—and this time he was not at all disappointed. Standing next to him on the step was exactly one half of a small child who had been divided neatly from top to bottom.

“Pardon me for staring,” said Milo, after he had been staring for some time, “but I’ve never seen half a child before.”

“It’s .58 to be precise,” replied the child from the left side of his mouth (which happened to be the only side of his mouth).

“I beg your pardon?” said Milo.

“It’s .58,” he repeated; “it’s a little bit morethan a half.”

“Have you always been that way?” asked Milo impatiently, for he felt that that was a needlessly fine distinction.

“My goodness, no,” the child assured him. “A few years ago I was just .42 and, believe me, that was terribly inconvenient.”

“What is the rest of your family like?” said Milo, this time a bit more sympathetically.

“Oh, we’re just the average family,” he said thoughtfully; “mother, father, and 2.58 children—and, as I explained, I’m the .58.”

“It must be rather odd being only part of a person,” Milo remarked.

“Not at all,” said the child. “Every average family has 2.58 children, so I always have someone to play with. Besides, each family also has an average of 1.3 automobiles, and since I’m the only one who can drive three tenths of a car, I get to use it all the time.”

“But averages aren’t real,” objected Milo; “they’re just imaginary.”

“That may be so,” he agreed, “but they’re also very useful at times. For instance, if you didn’t have any money at all, but you happened to be with four other people who had ten dollars apiece, then you’d each have an average of eight dollars. Isn’t that right?”

“I guess so,” said Milo weakly.

“Well, think how much better off you’d be, just because of averages,” he explained convincingly. “And think of the poor farmer when it doesn’t rain all year: if there wasn’t an average yearly rainfall of 37 inches in this part of the country, all his crops would wither and die.”

It all sounded terribly confusing to Milo, for he had always had trouble in school with just this subject.

“There are still other advantages,” continued the child. “For instance, if one rat were cornered by nine cats, then, on the average, each cat would be 10 per cent rat and the rat would be 90 per cent cat. If you happened to be a rat, you can see how much nicer it would make things.”

“But that can never be,” said Milo, jumping to his feet.

“Don’t be too sure,” said the child patiently, “for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see,” he went on, “it’s very much like your trying to reach Infinity. You know that it’s there, but you just don’t know where—but just because you can never reach it doesn’t mean that it’s not worth looking for.”

“I hadn’t thought of it that way,” said Milo, starting down the stairs. “I think I’ll go back now.”

“A wise decision,” the child agreed; “but try again someday—perhaps you’ll get much closer.” And, as Milo waved good-by, he smiled warmly, which he usually did on the average of 47 times a day.

“Everyone here knows so much more than I do,” thought Milo as he leaped from step to step. “I’ll have to do a lot better if I’m going to rescue the princesses.”

In a few moments he’d reached the bottom again and burst into the workshop, where Tock and the Humbug were eagerly watching the Mathemagician perform.

“Ah, back already,” he cried, greeting him with a friendly wave. “I hope you found what you were looking for.”

“I’m afraid not,” admitted Milo. And then he added in a very discouraged tone, “Everything in Digitopolis is much too difficult for me.”

The Mathemagician nodded knowingly and stroked his chin several times. “You’ll find,” he remarked gently, “that the only thing you can do easily is be wrong, and that’s hardly worth the effort.”

Milo tried very hard to understand all the things he’d been told, and all the things he’d seen, and, as he spoke, one curious thing still bothered him. “Why is it,” he said quietly, “that quite often even the things which are correct just don’t seem to be right?”

A look of deep melancholy crossed the Mathemagician’s face and his eyes grew moist with sadness. Everything was silent, and it was several minutes before he was able to reply at all.

“How very true,” he sobbed, supporting himself on the staff. “It has been that way since Rhyme and Reason were banished.”

“Quite so,” began the Humbug. “I personally feel that——”

“AND ALL BECAUSE OF THAT STUBBORN WRETCH AZAZ,” roared the Mathemagician, completely overwhelming the bug, for now his sadness had changed to fury and he stalked about the room adding up anger and multiplying wrath. “IT’S ALL HIS FAULT.”

“Perhaps if you discussed it with him——” Milo started to say, but never had time to finish.

“He’s much too unreasonable,” interrupted the Mathemagician again. “Why, just last month I sent him a very friendly letter, which he never had the courtesy to answer. See for yourself.”

He handed Milo a copy of the letter, which read:

“But maybe he doesn’t understand numbers,” said Milo, who found it a little difficult to read himself.

“NONSENSE!” bellowed the Mathemagician. “Everyone understands numbers. No matter what language you speak, they always mean the same thing. A seven is a seven anywhere in the world.”

“My goodness,” thought Milo, “everybody is so terribly sensitive about the things they know best.”

“With your permission,” said Tock, changing the subject, “we’d like to rescue Rhyme and Reason.”